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**Solving Equations with Variables on both Sides.**

What you’ll learn To solve equations with variables on both sides. To identify equations that are identities or have no solution. Identity: an equation that is true for every possible value of the variable.

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**What is the solution of 5x+2=2x+14 ?**

When you have variables in both sides you can use the properties of equality and inverse operations to write a series of simpler equivalents equations. What is the solution of 5x+2=2x+14 ? 5x+2=2x+14 Subtract 2x from each side -2x -2x Simplify 3x+2=14 Subtract 2 from each side -2 -2 Simplify. Divide each side by 3 3x=12 3 3 Simplify X=4 Check your answer: 5(4)+2=2(4)+14

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**Solve each equation. Check your answer.**

Your turn Solve each equation. Check your answer. a) 3x+4=5x-10 Answer: x=7 b) 5(y-4)=7(2y+1) Answer: Y=-3

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**+ Let’s do a word problem = 1.5p=1.25p+8 You solve it**

It takes a graphic designer 1.5 hours to make one page of a web site. Using new software, the designer could complete each page in 1.25 hours, but it takes 8 hours to learn the software. How many Web pages would the designer have to make in order to save time using the new software? Design time with new software Time to learn the software Current design time + = Let’s p= the number of pages the designer needs to make 1.5p=1.25p+8 You solve it And the answer is p=32, it will take the designer the same amount of time To make 32 web pages using either software. The designer Must make 33 pgs or more in order to save time using the new Software.

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**0.10 c+15=0.15c+10 Your turn Answer: c=100**

Pristine Printing will print business cards for $0.10 each plus a setup charge of $15. The Printing Place offers business cards for $0.15 each with a setup charge of $10. What number of business cards costs the same from either printer. 0.10 c+15=0.15c+10 Answer: c=100

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**Identities and Equations with no Solution**

What is the solution to each equation? Solve it by yourself a)10x+12=2(5x+6) b) 9m-4=-3m+5+12m 10x+12=10x+12 9m-4=9m+5 -4=5 Because this is always true. There are many solutions of the equation. The original equation is an identity. Because -4=5, The original equation has no solution.

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Your turn Match each equation with the appropriate number of solutions ? 3y-5=y+2y-9 2y+4=2(y+2) 2y-4=3y-5 Infinitely many solutions One solution No solution -5=9 4=4 1=y

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**Claswork odd Homework even**

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